I seem to remember once hearing it called a "closed time-like curve." That just seems silly, like it was technical for the sake of sounding technical.
Not at all, that's a real physics term. It's best known from Frank Tipler's 1974 paper "Rotating Cylinders and the Possibility of Global Causality Violation," which demonstrated that certain paths around a sufficiently massive rotating cylinder (which can be generalized to a massive rotating body such as a black hole) could become closed timelike curves, i.e. paths through spacetime that loop back and overlap themselves in the past. Intriguingly, this was seven years
after "Tomorrow is Yesterday" had shown the
Enterprise flung back in time by flying too close to a "black star," the term that was then used for the phenomena that John Wheeler would dub "black holes" less than a year later.
Terms such as "timelike" and "spacelike" are used for mathematical reasons; a timelike vector is one that behaves mathematically like time in Einsteinian relativity, while a spacelike vector is one that behaves mathematically like space in same. When talking in terms of the pure mathematics of it, you don't just call them "time" and "space" because mathematics is more about generalized, abstract patterns. And with reason, too. Often a set of mathematics that can be used to describe one thing can also turn out to be useful in describing something different. And that's the case here, too. In certain gravitationally warped regions of spacetime, like that around a rotating black hole or inside a Kerr ring singularity (like the "Kerr loop of superstring material" that created the time warp in "Yesterday's Enterprise," back when Trek tried to stay grounded in physics rather than making up random gibberish), you get what's called an inversion of spacelike and timelike axes: basically, time behaves like a dimension of space, allowing 2-way travel, while one dimension of space behaves like time, allowing only 1-way travel. This inverted spacetime is what makes time travel possible.
So normally a timelike vector is essentially a worldline, a plot of a particle's motion through space as time moves forward. But if you make time reversible, then that worldline can curve back, potentially crossing itself, and the timelike vector becomes a closed timelike curve. See?